# An Algebraic Framework for Runtime Verification

arXiv: https://arxiv.org/abs/1802.03775 · HTML: https://mlsanity.com/paper/1802.03775/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2018.

## Built on by (most cited first, 2 of 2)

- [Model-Free Reinforcement Learning for Symbolic Automata-encoded Objectives](https://mlsanity.com/paper/2202.02404/) (2022)
- [Declarative Scenario-based Testing with RoadLogic](https://mlsanity.com/paper/2603.09455/) (2026)

## Abstract (arXiv)

Runtime verification (RV) is a pragmatic and scalable, yet rigorous technique, to assess the correctness of complex systems, including cyber-physical systems (CPS). By measuring how robustly a CPS run satisfies a specification, RV allows in addition, to quantify the resiliency of a CPS to perturbations. In this paper we propose Algebraic Runtime Verification (ARV), a general, semantic framework for RV, which takes advantage of the monoidal structure of runs (w.r.t. concatenation) and the semiring structure of a specification automaton (w.r.t. choice and concatenation), to compute in an incremental and application specific fashion the resiliency measure. This allows us to expose the core aspects of RV, by developing an abstract monitoring algorithm, and to strengthen and unify the various qualitative and quantitative approaches to RV, by instantiating choice and concatenation with real-valued functions as dictated by the application. We demonstrate the power and effectiveness of our framework on two case studies from the automotive domain.